Question: Simplify; express your answer in exponential form. Assume $n\neq 0, x\neq 0$. $\dfrac{{n^{-4}}}{{(n^{5}x^{5})^{2}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${n^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${n^{-4} = n^{-4}}$ In the denominator, we can use the distributive property of exponents. ${(n^{5}x^{5})^{2} = (n^{5})^{2}(x^{5})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{n^{-4}}}{{(n^{5}x^{5})^{2}}} = \dfrac{{n^{-4}}}{{n^{10}x^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-4}}}{{n^{10}x^{10}}} = \dfrac{{n^{-4}}}{{n^{10}}} \cdot \dfrac{{1}}{{x^{10}}} = n^{{-4} - {10}} \cdot x^{- {10}} = n^{-14}x^{-10}$.